Optical Lattice Clock Magic-Wavelength Map (2D)

Trap Laser

Wavelength λ 813.4 nm

Trap depth U₀ 50 E_r

Include hyperpolarizability (deep-trap residual shift)

Clock Status

CLOCK LOCKED

Differential light shift Δν

0 Hz

Fractional shift Δν / ν₀

Detuning from nominal magic λ

0.0 nm

True zero-crossing λ at this U₀

813.400000 nm

Legend

Δν > 0 (blue-shifted)

Δν ≈ 0 (locked band)

Δν < 0 (red-shifted)

Current (λ, U₀) point — click/drag the map to move it

How it works

This is the 2D parameter-space companion to the 3D optical-lattice-clock simulator. Instead of rendering trapped atoms in a spatial lattice, it computes the same differential AC Stark shift formula directly on a 2D grid over the (wavelength λ, trap depth U₀) plane and paints it as a live heatmap — a genuine scalar field, not a camera view of anything:

Δν(λ, U₀) = SLOPE · (U₀ / U₀_ref) · (λ − λ_magic)  [+ hyperpolarizability term]
hyperpolarizability term = −h · U₀²   (survives even exactly at λ_magic, in deep traps)

Every pixel of the top map is this formula evaluated at that pixel's (λ, U₀) — white marks Δν ≈ 0 (the clock is insensitive to trap depth there), red/blue mark the sign and size of the drift. With hyperpolarizability off, that white band is a perfectly straight vertical line at λ = 813.4 nm for every trap depth: the ground/excited polarizabilities cancel regardless of intensity. Turning it on tilts the true zero-crossing very slightly — the "True zero-crossing λ" readout shows it to 10⁻⁶ nm precision, because the effect is genuinely that small (picometer-scale, matching how real strontium clocks report their magic wavelength).

Click or drag anywhere on the heatmap to move the current (λ, U₀) point directly — the sliders track it live, and vice versa.
Wavelength / trap-depth sliders — same physical knobs as the 3D version: detuning from 813.4 nm, and the trap's recoil-energy depth.
Hyperpolarizability toggle — adds the −h·U₀² term; watch the "True zero-crossing λ" stat move off 813.400000 nm by a few ten-thousandths of a nanometer as U₀ grows, and the lock status flip to DRIFTING once the residual at U₀=100 clears the 5 Hz threshold even sitting exactly on the nominal magic wavelength.

The strip below the heatmap re-draws the schematic ground/excited polarizability curves α_g(λ) and α_e(λ) whose crossing defines λ_magic in the first place, so you can see the field above and the curves that generate it side by side. Reference clock frequency ν₀ = 429,228,004,229,873.4 Hz is the CIPM-recommended value for the ⁸⁷Sr ¹S₀→³P₀ transition.

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Optical Lattice Clock — Magic-Wavelength Parameter Map (2D)